Why are these Grease Pencil objects moving together when I animate them?
The issue is that both of your objects are one single Grease Pencil object. If you look in the Outliner in your video (to the right), you will see that you have something highlighted in the list called Stroke. And both of these objects are part of it. Hence, why you can't move them independent of one another. If you want independent objects in 2D, you need to create a unique grease pencil object for each of them. This can be done in Object Mode, from the Add menu (Shift + a).